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Surface area using a net: triangular prism

Here are the steps to compute the surface area of a triangular prism: 1. Find the areas of each of the three rectangular faces, using the formula for the area of a rectangle: length x width. 2. Next, find the area of the two triangular faces, using the formula for the area of a triangle: 1/2 base x height. 3. Add the areas of all five faces together, and you're done!

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Video transcript

- [Instructor] What I want to do in this video is get some practice finding surface areas of figures by opening them up into what's called nets, and one way to think about it is if you had a figure like this, and if it was made out of cardboard and if you were to cut it, if you were to cut it right where I'm drawing this red, and also right over here and right over there and right over there and also in the back where you can't see it just now, it would open up into something like this. So if you were to open it up, it would open up into something like this, and when you open it up, it's much easier to figure out the surface area. So the surface area of this figure, when we open it up, we can just figure out the surface area of each of these regions. So let's think about it. So, what's, first of all, the surface area? What's the surface area of this right over here? Well, in the net that corresponds to this area. It's a triangle. It has a base of 12 and a height of eight. So this area right over here is going to be 1/2 times the base, so times 12, times the height, times eight. So this is the same thing as six times eight, which is equal to 48 whatever units, square units. This is gonna be units of area. So that's gonna be 48 square units. And up here is the exact same thing. That's the exact same thing. You can't see it in this figure. If it was transparent, if it was transparent, it would be this back side right over here. But that's also going to be 48, 48 square units. Now we can think about the areas of, I guess you could consider them to be the side panels. So that's a side panel right over there. It's 14 high and 10 wide. This is the other side panel. It's also, this length right over here is the same as this length, so it's also 14 high and 10 wide. So this side panel is this one right over here. And then you have one on the other side. And so the area of each of these, 14 times 10, they are 140 square units. This one is also 140 square units. And then finally we just have to figure out the area of, I guess you could say the base of this figure. So this whole region right over here, which is this area, which is that area right over there. And that's going to be 12 by 14. So this area is 12 times 14, which is equal to, let's see, 12 times 12 is 144, plus another 24, so it's 168. So the total area is going to be, let's see, if you add this one and that one, you get 96, 96 square units. The two magenta, I guess you could say, side panels, 140 plus 140, that's 280. 280. And then you have this base that comes in at 168. Want me do that same color? 168, 168. Add them all together and we get the surface area for the entire figure, and it was super valuable to open it up into the net 'cause we could make sure we got all of the sides. We didn't have to kind of rotate it in our brains, although you could do that as well. So six plus zero plus eight is 14. Regroup the one 10 to the tens place. So it's now one 10. So one plus nine is 10, plus eight is 18, plus six is 24. And then you have, oops. And then you have two plus two plus one is five. So the surface area of this figure is 544, 544 square units.